Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain.
Phys Rev E. 2018 Jan;97(1-1):012310. doi: 10.1103/PhysRevE.97.012310.
The influence of zealots on the noisy voter model is studied theoretically and numerically at the mean-field level. The noisy voter model is a modification of the voter model that includes a second mechanism for transitions between states: Apart from the original herding processes, voters may change their states because of an intrinsic noisy-in-origin source. By increasing the importance of the noise with respect to the herding, the system exhibits a finite-size phase transition from a quasiconsensus state, where most of the voters share the same opinion, to one with coexistence. Upon introducing some zealots, or voters with fixed opinion, the latter scenario may change significantly. We unveil new situations by carrying out a systematic numerical and analytical study of a fully connected network for voters, but allowing different voters to be directly influenced by different zealots. We show that this general system is equivalent to a system of voters without zealots, but with heterogeneous values of their parameters characterizing herding and noisy dynamics. We find excellent agreement between our analytical and numerical results. Noise and herding or zealotry acting together in the voter model yields a nontrivial mixture of the scenarios with the two mechanisms acting alone: It represents a situation where the global-local (noise-herding) competition is coupled to a symmetry breaking (zealots). In general, the zealotry enhances the effective noise of the system, which may destroy the original quasiconsensus state, and can introduce a bias towards the opinion of the majority of zealots, hence breaking the symmetry of the system and giving rise to new phases. In the most general case we find two different transitions: a discontinuous transition from an asymmetric bimodal phase to an extreme asymmetric phase and a second continuous transition from the extreme asymmetric phase to an asymmetric unimodal phase.
狂热分子对嘈杂投票者模型的影响在平均场水平上进行了理论和数值研究。嘈杂投票者模型是投票者模型的一种修改，其中包括状态之间转换的第二种机制：除了原始的从众过程之外，由于起源于固有噪声的源，选民可能会改变其状态。通过增加噪声相对于从众的重要性，系统表现出从准共识状态到共存的有限尺寸相变，在准共识状态中，大多数选民具有相同的观点。引入一些狂热分子，或具有固定观点的选民，可能会显著改变后者的情况。我们通过对投票者的全连接网络进行系统的数值和分析研究，允许不同的投票者直接受到不同狂热分子的影响，揭示了新的情况。我们表明，这个一般系统等效于没有狂热分子的投票者系统，但具有描述从众和噪声动态的参数的异质值。我们发现我们的分析和数值结果之间有极好的一致性。在投票者模型中，噪声和从众或狂热分子一起作用会产生两个单独作用的机制的情况的非平凡混合物：它代表了全局-局部（噪声-从众）竞争与对称性破缺（狂热分子）耦合的情况。一般来说，狂热分子会增强系统的有效噪声，这可能会破坏原始的准共识状态，并可能导致大多数狂热分子的观点出现偏差，从而打破系统的对称性并产生新的相。在最一般的情况下，我们发现了两种不同的转变：从不对称双峰相到极端不对称相的不连续转变和从极端不对称相到不对称单峰相的第二个连续转变。
